Question

If $L_1$ is the equation of the chord of the circle $x^2+y^2-6x-4y+4=0$ passing through $(3,4)$ and farthest from the centre, then which of the following is/are correct?

• A. Equation of $L_1:y=4$
• B. Equation of $L_1:2x-y=2$
• C. Length of the chord is $2\sqrt{5}$
• D. Length of the chord is $\sqrt{5}$

Answer 1

Answer: (A), (C)

The correct options are
A Equation of $L_1:y=4$
C Length of the chord is $2\sqrt{5}$

Given circle is
$x^2+y^2-6x-4y+4=0$
$C=(3,2),r=3$
The chord which is farthest from the centre $(3,2)$ and passing through $(3,4)$ is the chord which has midpoint at $(3,4)$, so
$T=S_1\Rightarrow 3x+4y-3(x+3)-2(y+4)+4=9+16-18-16+4\Rightarrow 2y=8\therefore y=4$

Length of chord with given midpoint
$=2\sqrt{|S_1|}=2\sqrt{5}$